Bounded rank perturbations of matrix pencils without nontrivial invariant factors

Abstract

In this paper, we solve the bounded rank perturbation problem for matrix pencils without nontrivial homogeneous invariant factors, over arbitrary fields. The solution is based on reducing the problem to two minimal case matrix pencil completion problems. If there are no nontrivial homogeneous invariant factors involved, these two minimal completion problems allow treating column and row minimal indices separately. This is an example of the utility of completion tools in perturbation problems, when dealing with matrix pencils.